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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> * Copyright (c) 2010-2011, NVIDIA Corporation</span>
<a name="l00003"></a>00003 <span class="comment"> * All rights reserved.</span>
<a name="l00004"></a>00004 <span class="comment"> *</span>
<a name="l00005"></a>00005 <span class="comment"> * Redistribution and use in source and binary forms, with or without</span>
<a name="l00006"></a>00006 <span class="comment"> * modification, are permitted provided that the following conditions are met:</span>
<a name="l00007"></a>00007 <span class="comment"> *   * Redistributions of source code must retain the above copyright</span>
<a name="l00008"></a>00008 <span class="comment"> *     notice, this list of conditions and the following disclaimer.</span>
<a name="l00009"></a>00009 <span class="comment"> *   * Redistributions in binary form must reproduce the above copyright</span>
<a name="l00010"></a>00010 <span class="comment"> *     notice, this list of conditions and the following disclaimer in the</span>
<a name="l00011"></a>00011 <span class="comment"> *     documentation and/or other materials provided with the distribution.</span>
<a name="l00012"></a>00012 <span class="comment"> *   * Neither the name of NVIDIA Corporation nor the</span>
<a name="l00013"></a>00013 <span class="comment"> *     names of its contributors may be used to endorse or promote products</span>
<a name="l00014"></a>00014 <span class="comment"> *     derived from this software without specific prior written permission.</span>
<a name="l00015"></a>00015 <span class="comment"> *</span>
<a name="l00016"></a>00016 <span class="comment"> * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS &quot;AS IS&quot; AND</span>
<a name="l00017"></a>00017 <span class="comment"> * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED</span>
<a name="l00018"></a>00018 <span class="comment"> * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE</span>
<a name="l00019"></a>00019 <span class="comment"> * DISCLAIMED. IN NO EVENT SHALL &lt;COPYRIGHT HOLDER&gt; BE LIABLE FOR ANY</span>
<a name="l00020"></a>00020 <span class="comment"> * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES</span>
<a name="l00021"></a>00021 <span class="comment"> * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;</span>
<a name="l00022"></a>00022 <span class="comment"> * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND</span>
<a name="l00023"></a>00023 <span class="comment"> * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span>
<a name="l00024"></a>00024 <span class="comment"> * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS</span>
<a name="l00025"></a>00025 <span class="comment"> * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span>
<a name="l00026"></a>00026 <span class="comment"> */</span>
<a name="l00027"></a>00027 
<a name="l00028"></a>00028 
<a name="l00029"></a>00029 <span class="keyword">namespace </span>nih {
<a name="l00030"></a>00030 
<a name="l00031"></a>00031 <span class="comment">//</span>
<a name="l00032"></a>00032 <span class="comment">// Evaluate a DIM-dimensional Brownian bridge of length L at time t,</span>
<a name="l00033"></a>00033 <span class="comment">// using a black-box Gaussian generator.</span>
<a name="l00034"></a>00034 <span class="comment">//</span>
<a name="l00035"></a>00035 <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Generator, u<span class="keywordtype">int</span>32 DIM&gt;
<a name="l00036"></a><a class="code" href="group__processes.html#gabb2dd2ed5d619ca9c891ed4ce050fa6a">00036</a> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> <a class="code" href="group__processes.html#gabb2dd2ed5d619ca9c891ed4ce050fa6a">brownian_bridge</a>(
<a name="l00037"></a>00037     <span class="keyword">const</span> uint32        L,
<a name="l00038"></a>00038     <span class="keyword">const</span> uint32        t,
<a name="l00039"></a>00039     Generator           gaussian)
<a name="l00040"></a>00040 {
<a name="l00041"></a>00041     <span class="comment">// check whether the origin is being retrived</span>
<a name="l00042"></a>00042     <span class="keywordflow">if</span> (t == 0) <span class="keywordflow">return</span> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a>(0.0f);
<a name="l00043"></a>00043 
<a name="l00044"></a>00044     <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> p1(0.0f);
<a name="l00045"></a>00045     <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> p2 = gaussian.next() * sqrtf(<span class="keywordtype">float</span>(L));
<a name="l00046"></a>00046 
<a name="l00047"></a>00047     <span class="comment">// check whether the last point is being retrived</span>
<a name="l00048"></a>00048     <span class="keywordflow">if</span> (t == L) <span class="keywordflow">return</span> p2;
<a name="l00049"></a>00049 
<a name="l00050"></a>00050     <span class="comment">// perform a binary search to get to instant t</span>
<a name="l00051"></a>00051     <span class="keyword">const</span> uint32 log_L = log2( L );
<a name="l00052"></a>00052 
<a name="l00053"></a>00053     uint32 t1 = 0;
<a name="l00054"></a>00054     uint32 t2 = L;
<a name="l00055"></a>00055 
<a name="l00056"></a>00056     <span class="keywordflow">for</span> (uint32 l = 0; l &lt; log_L; ++l)
<a name="l00057"></a>00057     {
<a name="l00058"></a>00058         <span class="keyword">const</span> uint32 M  = 1u &lt;&lt; l;
<a name="l00059"></a>00059         <span class="keyword">const</span> uint32 DT = L/M;
<a name="l00060"></a>00060 
<a name="l00061"></a>00061         <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> pm = (p1 + p2)*0.5f + gaussian.next() * sqrtf(<span class="keywordtype">float</span>(L/(2*M)));
<a name="l00062"></a>00062 
<a name="l00063"></a>00063         <span class="keyword">const</span> uint32 tm = (t1 + t2)/2;
<a name="l00064"></a>00064 
<a name="l00065"></a>00065         <span class="keywordflow">if</span> (t == im)
<a name="l00066"></a>00066         {
<a name="l00067"></a>00067             p2 = pm;
<a name="l00068"></a>00068             <span class="keywordflow">break</span>;
<a name="l00069"></a>00069         }
<a name="l00070"></a>00070 
<a name="l00071"></a>00071         <span class="keywordflow">if</span> (t &lt; im)
<a name="l00072"></a>00072         {
<a name="l00073"></a>00073             p2 = pm;
<a name="l00074"></a>00074             t2 = tm;
<a name="l00075"></a>00075         }
<a name="l00076"></a>00076         <span class="keywordflow">else</span>
<a name="l00077"></a>00077         {
<a name="l00078"></a>00078             p1 = pm;
<a name="l00079"></a>00079             t1 = tm;
<a name="l00080"></a>00080         }
<a name="l00081"></a>00081     }
<a name="l00082"></a>00082     <span class="keywordflow">return</span> p2;
<a name="l00083"></a>00083 }
<a name="l00084"></a>00084 
<a name="l00085"></a>00085 <span class="comment">//</span>
<a name="l00086"></a>00086 <span class="comment">// A simple utility function to generate a DIM-dimensional Gaussian point</span>
<a name="l00087"></a>00087 <span class="comment">// using the i-th point of a sample sequence, shifted by a Cranley-Patterson</span>
<a name="l00088"></a>00088 <span class="comment">// rotation.</span>
<a name="l00089"></a>00089 <span class="comment">//</span>
<a name="l00090"></a>00090 <span class="keyword">template</span> &lt;u<span class="keywordtype">int</span>32 DIM, <span class="keyword">typename</span> Distribution, <span class="keyword">typename</span> Sampler_type&gt;
<a name="l00091"></a><a class="code" href="group__processes.html#ga1e80545c2d9cb0ccdc535bd7bbc6b003">00091</a> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> <a class="code" href="group__processes.html#ga1e80545c2d9cb0ccdc535bd7bbc6b003">generate_point</a>(
<a name="l00092"></a>00092     Sampler_type&amp;             sampler,
<a name="l00093"></a>00093     Distribution&amp;             gaussian)
<a name="l00094"></a>00094 {
<a name="l00095"></a>00095     <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> pt;
<a name="l00096"></a>00096     <span class="keywordflow">for</span> (uint32 d = 0; d &lt; DIM; ++d)
<a name="l00097"></a>00097         pt[d] = gaussian.next( sampler );
<a name="l00098"></a>00098 
<a name="l00099"></a>00099     <span class="keywordflow">return</span> pt;
<a name="l00100"></a>00100 }
<a name="l00101"></a>00101 
<a name="l00102"></a>00102 <span class="comment">//</span>
<a name="l00103"></a>00103 <span class="comment">// Evaluate the i/N-th DIM-dimensional Brownian bridge of length L at time t.</span>
<a name="l00104"></a>00104 <span class="comment">// The bridges are created using L copies of a DIM-dimensional Sobol sequence,</span>
<a name="l00105"></a>00105 <span class="comment">// first permuted and then shifted through Cranley-Patterson rotations.</span>
<a name="l00106"></a>00106 <span class="comment">// The vector of permutations must contain L permutations of the indices [0,N-1],</span>
<a name="l00107"></a>00107 <span class="comment">// and the vector of rotations must contain L * (DIM + (DIM &amp; 1)) entries.</span>
<a name="l00108"></a>00108 <span class="comment">//</span>
<a name="l00109"></a>00109 <span class="keyword">template</span> &lt;u<span class="keywordtype">int</span>32 DIM, <span class="keyword">typename</span> Sequence, <span class="keyword">typename</span> Distribution&gt;
<a name="l00110"></a><a class="code" href="group__processes.html#gadd2480f0c83af4a386b888ed7ed8e955">00110</a> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> <a class="code" href="group__processes.html#gabb2dd2ed5d619ca9c891ed4ce050fa6a">brownian_bridge</a>(
<a name="l00111"></a>00111     Distribution&amp;               gaussian,
<a name="l00112"></a>00112     <span class="keyword">const</span> <span class="keywordtype">float</span>                 sigma,
<a name="l00113"></a>00113     <span class="keyword">const</span> uint32                N,
<a name="l00114"></a>00114     <span class="keyword">const</span> uint32                i,
<a name="l00115"></a>00115     <span class="keyword">const</span> uint32                L,
<a name="l00116"></a>00116     <span class="keyword">const</span> uint32                t,
<a name="l00117"></a>00117     <span class="keyword">const</span> Sequence&amp;             sequence)
<a name="l00118"></a>00118 {
<a name="l00119"></a>00119     <span class="comment">// check whether the origin is being retrived</span>
<a name="l00120"></a>00120     <span class="keywordflow">if</span> (t == 0) <span class="keywordflow">return</span> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a>(0.0f);
<a name="l00121"></a>00121 
<a name="l00122"></a>00122     <span class="keyword">const</span> uint32 EVEN_DIM = DIM + (DIM &amp; 1);
<a name="l00123"></a>00123 
<a name="l00124"></a>00124     <span class="keyword">typedef</span> <span class="keyword">typename</span> Sequence::Sampler_type Sampler_type;
<a name="l00125"></a>00125 
<a name="l00126"></a>00126     <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> p1(0.0f);
<a name="l00127"></a>00127     <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> p2 = generate_point&lt;DIM&gt;( sequence.instance( i, 0 ), gaussian ) * sqrtf(<span class="keywordtype">float</span>(L)) * sigma;
<a name="l00128"></a>00128 
<a name="l00129"></a>00129     <span class="comment">// check whether the last point is being retrived</span>
<a name="l00130"></a>00130     <span class="keywordflow">if</span> (t == L) <span class="keywordflow">return</span> p2;
<a name="l00131"></a>00131 
<a name="l00132"></a>00132     <span class="comment">// perform a binary search to get to instant t</span>
<a name="l00133"></a>00133     <span class="keyword">const</span> uint32 log_L = log2( L );
<a name="l00134"></a>00134 
<a name="l00135"></a>00135     uint32 t1 = 0;
<a name="l00136"></a>00136     uint32 t2 = L;
<a name="l00137"></a>00137 
<a name="l00138"></a>00138     <span class="keywordflow">for</span> (uint32 l = 0; l &lt; log_L; ++l)
<a name="l00139"></a>00139     {
<a name="l00140"></a>00140         <span class="keyword">const</span> uint32 M  = 1u &lt;&lt; l;
<a name="l00141"></a>00141         <span class="keyword">const</span> uint32 DT = L/M;
<a name="l00142"></a>00142 
<a name="l00143"></a>00143         <span class="keyword">const</span> uint32 tm = (t1 + t2)/2;
<a name="l00144"></a>00144 
<a name="l00145"></a>00145         <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector&lt;float,DIM&gt;</a> pm = (p1 + p2)*0.5f +
<a name="l00146"></a>00146             generate_point&lt;DIM&gt;( sequence.instance( i, tm ), gaussian ) * sqrtf(<span class="keywordtype">float</span>(L/(2*M))) * sigma;
<a name="l00147"></a>00147 
<a name="l00148"></a>00148         <span class="keywordflow">if</span> (t == tm)
<a name="l00149"></a>00149         {
<a name="l00150"></a>00150             p2 = pm;
<a name="l00151"></a>00151             <span class="keywordflow">break</span>;
<a name="l00152"></a>00152         }
<a name="l00153"></a>00153 
<a name="l00154"></a>00154         <span class="keywordflow">if</span> (t &lt; tm)
<a name="l00155"></a>00155         {
<a name="l00156"></a>00156             p2 = pm;
<a name="l00157"></a>00157             t2 = tm;
<a name="l00158"></a>00158         }
<a name="l00159"></a>00159         <span class="keywordflow">else</span>
<a name="l00160"></a>00160         {
<a name="l00161"></a>00161             p1 = pm;
<a name="l00162"></a>00162             t1 = tm;
<a name="l00163"></a>00163         }
<a name="l00164"></a>00164     }
<a name="l00165"></a>00165     <span class="keywordflow">return</span> p2;
<a name="l00166"></a>00166 }
<a name="l00167"></a>00167 
<a name="l00168"></a>00168 } <span class="comment">// namespace nih</span>
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